Abstract
A non-uniqueness study for a hydromechanical boundary value problem is performed. A fully saturated porous medium is considered using an elasto-plastic constitutive equations to describe the mechanical behavior of the skeleton. A real hydromechanical experiment which consists in a hollow cylinder test on a Boom Clay sample is modelled. It is shown that the time step discretisation of the numerical problem has an effect on the initialisation of the Newton-Raphson algorithm on a given time step. Different solutions for the same initial boundary value problem can consequently be found.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Barnichon JD (1998) Finite element modelling in structural and petroleum geology. Ph.D. thesis, Université de Liège Faculté des Sciences Appliquées
Bésuelle P, Chambon R, Collin F (2006) Switching deformation modes in post-localization solutions with quasi-brittle material. Mech Mater struct 1(7):1115–1134
Chambon R, Caillerie D, El Hassan N (1998) One-dimensional localisation studied with a second grade model. Eur J Mech A Solids 4:637–656
Chambon R, Crochepeyre S, Charilier R (2001) An algorithm and a method to search bifurcation points in non-linear problems. Int J Numer Meth Eng 51(3):315–332
Collin F, Chambon R, Charlier R (2006) A finite element method for poro mechanical modelling of geotechnical problems using local second gradient models. Int J Numer Meth Eng 65:1749–1772
Germain P (1973) The method of the virtual power in continuum mechanics. Part 2: microstructure. J Appl Math 25(3):556–575
Hill R (1978) Aspects of invariance in solid mechanics. Adv Appl Mech 18:1–75
Horseman ST, Winter MG, Entwistle DC (1987) Geotechnical characterization of boom clay in relation to the disposal of radioactive waste (page 87). Technical report, Commission of the European Communities, EUR 10987
Labiouse V, Sauthier C, You S (2014) Hollow cylinder simulation experiments of galleries in boom clay formation. Rock Mech Rock Eng 47:43–45
Mindlin RD (1964) Micro-structure in linear elasticity. Arch Ration Mech Anal 16(1):51–78
Ortiz M, Simo JC (1986) An analysis of a new class of integration algorithms for elastoplastic constitutive relations. Int J Numer Meth Eng 23(3):353–366
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Marinelli, F., Sieffert, Y., Chambon, R. (2015). Hydromechanical Modelling of an Initial Boundary Value Problem: Studies of Non-uniqueness with a Second Gradient Continuum. In: Chau, KT., Zhao, J. (eds) Bifurcation and Degradation of Geomaterials in the New Millennium. IWBDG 2014. Springer Series in Geomechanics and Geoengineering. Springer, Cham. https://doi.org/10.1007/978-3-319-13506-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-13506-9_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13505-2
Online ISBN: 978-3-319-13506-9
eBook Packages: EngineeringEngineering (R0)